Question

What is the coterminal angle of csc(-660 degrees)

Answer 1

We need to simplify the initial expression as follows

`\begin{gathered} \csc (-660degree) \\ =(1)/(\sin(-660degree)) \\ =(1)/(\sin(-300-360degree)) \\ =(1)/(\sin(-300degree)) \\ =-(1)/(\sin(300degree)) \end{gathered}`

Then, in a diagram

The blue angle is a 300°, then we found out that sin(300°)= -sin(60°), as shown in the figure

Then

`\begin{gathered} -(1)/(\sin(300degree))=\frac{1}{\sin (60\text{degre}e)} \\ \Rightarrow\csc (-660degree)=(1)/(\sin (60degree)) \end{gathered}`

Therefore, the coterminal angle is +60°